Kadriorg Palace, a baroque beauty built by Peter the Great between 1718 and 1736, houses a branch of the Art Museum of Estonia devoted to Dutch, German and Italian paintings from the 16th to the 18th centuries, and Russian works from the 18th to early 20th centuries (check out the decorative porcelain with communist imagery upstairs). The pink palace is exactly as frilly and fabulous as it ought to be, and there’s a handsome French-style formal garden at the rear.
Take tram 1 or 3 from the centre to the 'Kardiorg' stop to reach the park, then follow the signs. Joint tickets with the Mikkel Museum (adult/reduced €13/9) are available, as are tickets that cover all five branches of the Art Museum across the city (€36/24).
